I do not quite understand the construction of Voevodsky motives yet. Let $ k$ be a field (possibly not algebraically closed), $ X$ be a connected smooth projective $ k$ -scheme. Does the motive of $ X$ in the abelian category of pure numerical motives determine its Voevodsky motive? The coefficients are either $ \mathbb{Z}$ or $ \mathbb{Q}$ (the answer should address both). Please provide a reference.

# Tag: motive

## $p$-adic realisation of Kummer motive and Frobenius matrix

Suppose $ M$ is an object in the abelian category of mixed Tate motives over $ \mathbb{Q}$ , and it is an extension of $ \mathbb{Q}(0)$ by $ \mathbb{Q}(1)$ \begin{equation} 0 \rightarrow \mathbb{Q}(1) \rightarrow M \rightarrow \mathbb{Q}(0) \rightarrow 0. \end{equation} Suppose the Hodge realisation of $ M$ is the one associated to $ \log u, u \in \mathbb{Q}^*$ , i.e. $ u$ is a nonzero rational number. Suppose $ p$ is an unramified prime of $ M$ , and in the $ p$ -adic realisation of $ M$ , what is the matrix associated to the geometric Frobenius?

The matrix must be of the form \begin{pmatrix} 1, ~~~0 \ *, 1/p \end{pmatrix} but is the unknown $ *$ in the matrix just the $ p$ -adic value of $ \log u$ , i.e. the $ p$ -adic logarithm valued at $ u$ .

Remark, I do not understand the $ p$ -adic realisations of the mixed Tate motives very well, so the statement of this question might not be very rigorous. References about the $ p$ -adic realisations of mixed Tate motives are welcomed.

## What is the motive behind this shockingly annoying decision by Youtube? [on hold]

I am trying to understand what motives a multi-billion dollar platform, that employs thousands of smart people to perfect its services, might have to make the decision to completely and utterly destroy the user experience.

I am talking about this stuff:

I’m trying to watch a goal by Messi. The video is 1 minute and 10 seconds long. We are at the 49th second now, and the video is literally blocking me from watching the goal.

What in the world is this? How can such an atrocious decision even be made, from any sort of logical standpoint? Why is Youtube preventing me from watching their own videos? Why are they intentionally making their own product worse?

It’s one thing if there was some button that I could click that said “*tired of having your video blocked? Click here and pay some money and you’ll be rid of it!*“… I mean, that would be a douchy move, but it would at least make some sense. But they don’t even do that, they literally just made their product worse without giving me an ability to change it.

WTF?

## [ Politics ] Open Question : Can you believe that our government has found “no motive” for the Las Vegas shooter’s murder spree?

Sorry, but I ALWAYS follow up on these mass shootings and the criminal who did them. I have a need to know his history. I CANNOT ACCEPT that someone so heavily armed and such a well planned and staged series of murders had absolutely no motive whatsoever in doing this. As though this was just circumstance or a joke.